Journal of Combinatorics

Volume 3 (2012)

Number 4

Nodal domain and eigenvalue multiplicity of graphs

Pages: 609 – 622

DOI: https://dx.doi.org/10.4310/JOC.2012.v3.n4.a1

Authors

Hao Xu (Department of Mathematics, Harvard University, Cambridge, Mass., U.S.A)

Shing-Tung Yau (Department of Mathematics, Harvard University, Cambridge, Mass., U.S.A)

Abstract

We give a uniform proof of the upper and lower bounds of strong nodal domains for generalized Laplacians of discrete graphs. We also study the set of all possible numbers of strong nodal domains and the maximum multiplicity sequence of spectra.

Keywords

nodal domain, eigenvalue multiplicity, Laplacian

2010 Mathematics Subject Classification

05C50, 15A18

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Published 21 February 2013